There are many different designs of tilt sensors or angular sensors or inclinometers and accelerometers and some of them are already commercialized. It is a well known problem for available sensors that they can measure either tilt (inclination angle) or horizontal acceleration, but not both concurrently, because acceleration can generate a tilt signal in a tilt sensor:β=arc tan (a/g)where β is the tilt signal angle, a is the horizontal linear acceleration and g is the gravitational acceleration. In the figures that follow, gravitational acceleration g is directed toward the bottom of the page. Likewise, tilt can generate a horizontal acceleration signal in an accelerometer.
In the case where both tilt and acceleration occur concurrently, however, legacy sensors cannot distinguish between tilt and acceleration and, therefore, cannot measure the signal generated by tilt and the signal generated by acceleration separately in dynamic environment. For example, a tilt sensor or an accelerometer or both are mounted in a moving vehicle, which is a dynamic environment. It is very difficult to measure either tilt or acceleration or both of them separately because of interference from tilt with acceleration and interference of acceleration with tilt. Robert L. Forward designed a method to directly measure these two signals in separate forms. However, he further stated that this method was only academically correct. Robert L. Forward proposed another method to separate these two terms by measuring the resonant frequencies of the sensors and determine the tensor components. French, et al., also used resonant frequency to decrease the noise brought by the horizontal acceleration to measure gravitational field. Dosch, et al., calculated the gravitational field with better accuracy by accounting for undesired accelerations picked up by accelerometers having input axes that are not parallel to the gradiometer disc.
The remaining problem of how to accurately measure the tilt and horizontal acceleration in separate terms and at the same time, however, is yet to be completely resolved. Progress has been made by the present inventor, as shown by U.S. Pat. No. 6,282,804 to the present invention and co-pending U.S. patent application Ser. No. 12/625,333 to the present inventor.